Hi cavediver, have you already looked into hyperincursive thoery. If it looks credible to you, then I suggest you start a thread about it explaining selfrefferential equations and the like. Like I said it is too complicated for me to explain.
As such I would expect it to be difficult identify and to contain.
Yep :) We tend to discover new particles by their distinct decay processes - i.e. what we actually "see" are the decay products, and their characteristics are used to infer the characteristics of the parent particle. Stable particles don't decay much for obvious reasons :) But they can be revealed by the *missing* characteristics following a collision. Unfortunately, this is also how we can detect for extra dimensions, so it's not an easy task differentiating all of these possibilities. But with some good luck it can be done...
Do you expect the quarks and leptons to be broken down into sub-sub-atomic particles?
Heh, heh - I've just noticed the name of the guy who started this thread. Shall we offer a prize to the first EvC'er who can explain why that name is particularly appropriate to a thread on WIMPs? :D but first you have to see what I'm getting at ;)
Thanks Cavediver and Son Goku, for, um, fielding that question ...
But they can be revealed by the *missing* characteristics following a collision. Unfortunately, this is also how we can detect for extra dimensions, so it's not an easy task differentiating all of these possibilities. But with some good luck it can be done...
See SG's earlier post.
Son Goku writes:
Message 14: The first being and I'm not sure how to say this, the proton is not really "made" of three quarks. Rather the proton is a state produced by the interaction of about eleven different quantum fields. Three of those fields, if they didn't interact with the others, that is if they were free, would have excitations which we call quarks. So those fields are called the quark fields. However since the fields do interact, this picture isn't accurate and the fields never possess those excitations we call the quark particle
Virtual particles? So is the proton a particle or the intersection of these fields: wherever they intersect in the right pattern there be protons? I thought Feynman demonstrated that particles were the best explanation?
And is this how we get to multi-dimensions with string theory?
So is the proton a particle or the intersection of these fields
It's both. A particle resulting from the interactions of fields.
I thought Feynman demonstrated that particles were the best explanation?
Particles are basic excitations of the fields and provided that the fields are not too "active" they may be used to provide a description of the fields detailed enough to compare with experiment. Concentrating on the particles also makes calculations simpler and means terms in the calculation can be represented by diagrams. This was Feynman's method.
And is this how we get to multi-dimensions with string theory?
No, the extra dimensions of String theory arise from different considerations.
Hopefully I can outline things in decent way, although I've never actually been in String research.
First of all you should know of a process called quantization. This is a standard mathematical procdeure where one turns a classical theory into a quantum theory. It twins a classical theory with a quantum theory, essentially giving a quantum version of that classical theory.
Now when a physicist speaks of something like quantum field theory and String theory, we are not to be taken at our word. The objects these theories describe are not fields or strings. Rather those names refer to the kind of classical object described by the classical twin of these theories. For instance quantum field theory should be labelled the less catchy "Theory which is the quantum twin of a classical theory that describes feilds".
Too cut a (very) long story short, several people for various reasons, came to the conclusion that a theory of Strings was the best way to incorporate gravity into a quantum mechanical framework.
In order to find such a String Theory physicists used the technique of quantization to start with a classical theory describing strings and end up with its quantum twin which should describe gravity. However it was found that if one sticks to four spacetime dimensions this doesn't really work. The quantization process turns gives an inconsistent theory as the twin to the classical theory of strings. If one wants a mathematically healthy theory to be the result of the quantization process, you must crank up the number of dimensions.
The simple answer is that when you formulate string theory in d space-time dimensions, you obtain an anomaly which destroys the physical characteristics of the theory - however the anomaly contains a factor of (d-10), so when d=10, the anomaly disappears. This is quite unusal - most physical theories work equally well in any number of dimensions - GR, electromagnetism, etc, and thus they give no clues as to what the dimension of space-time should be. One exception is Supergravity, and interestingly string theory and Supergravity have now revealed themselves as simply different perspectives of the same (M) theory, despite very different origins, and they are the two trheories that actually give important clues to the dimension of space-time.
That's the first time I've had a tiny hint of what the math is like for M( etc) theory.
I know that the whole thing would be incomprehensible to me but having just a hint is good.
Can we take the next tiny step in adding a bit more detail? I know what some equations look like (Schroedinger's for example) and even understand a bit of what goes on there. What does the math we are talking about "look like"? Is it one equation? Lots? Does it have many variables, parameters? a few?
What does the math we are talking about "look like"? Is it one equation? Lots?
We can start with a single Lagrangian and go on a long journey of discovery. It will involve many equations and expressions.
Can we take the next tiny step in adding a bit more detail?
:eek: I'm trying to work out how and it comes back to me why no-matter how many Mickey Mouse undergrad string theory courses are introduced, it is most definitely an advanced post-graduate subject. To understand the fuss and get that 'wow' factor, you really need to be comfortable with Lagrangian formulations of General Relativity and Quantum Field Theory, and have some knowledge of the Renormalisation Group. And this is just the very beginning!!
But it is a challenge, so I may well have a go. It may be good to start with an *easy* topic like Hilbert's Lagrangian formulation of General Relativity. How familiar are you with Lagrangian mechanics? Given the fundemental nature of this, it may even be good to start here. This could be a long journey...